Question: A circle has a sector with area $15\pi$ and central angle $54^\circ$. What is the area of the circle? ${100\pi}$ $\color{#9D38BD}{54^\circ}$ ${15\pi}$
Answer: The ratio between the sector's central angle $\theta$ and $360^\circ$ is equal to the ratio between the sector's area, $A_s$ , and the whole circle's area, $A_c$ $\dfrac{\theta}{360^\circ} = \dfrac{A_s}{A_c}$ $\dfrac{54^\circ}{360^\circ} = 15\pi \div A_c$ $\dfrac{3}{20} = 15\pi \div A_c$ $A_c \times \dfrac{3}{20} = 15\pi$ $A_c = 15\pi \times \dfrac{20}{3}$ $A_c = 100\pi$